A works five times as fast as B, and B works five times as fast as C. A, B and C, together with D, can finish a piece of work in 15 days. If D alone can finish the work in 60 days, in how many days will A alone finish the work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24.8 days
Each rate can be written in terms of C's rate. The four together do \(\frac{1}{15}\) of the work a day, so taking away D's share leaves the rate of A, B and C.
Let C do \(c\) of the work per day; then B does \(5c\) and A does \(25c\)
A, B and C together: \(25c+5c+c=31c\)
\(\displaystyle 31c=\frac{1}{15}-\frac{1}{60}=\frac{4-1}{60}=\frac{1}{20}\), so \(\displaystyle c=\frac{1}{620}\)
A's one-day work \(\displaystyle =25c=\frac{25}{620}=\frac{5}{124}\)
A alone takes \(\displaystyle \frac{124}{5}=24.8\) days
A alone finishes the work in 24.8 days.